HomePricing
Sign InJoin

Exponents - Fractional Exponents with Non-Square Integer Base - Exponent to Factored Exponent (Level 2)

This math topic focuses on practicing the manipulation of fractional exponents with non-square integer bases. Specifically, students learn how to simplify expressions by factoring the base before applying the fractional exponent. Problems involve converting a base into its factored form and thereafter applying fractional exponents like \( \frac{1}{2}, \frac{1}{3}, \text{ or } \frac{1}{4} \) to these factored forms. Each question is designed to help students understand how factorization can simplify the calculation of powers, enhancing their skills in handling exponents and powers involving integers and fractions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

View Unit

Fractional Exponents with Non-Square Integer Base - Exponent to Factored Exponent

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Factor the base number to make it easier to solve

45(12)45^{(\frac{1}{2})}

Exponents - Fractional Exponents with Non-Square Integer Base - Exponent to Factored Exponent Worksheet

Mobius Math Club logo
Math worksheet on 'Exponents - Fractional Exponents with Non-Square Integer Base - Exponent to Factored Exponent (Level 2)'. Part of a broader unit on 'Exponents - Fractional Bases and Exponents - Practice' Learn online: app.mobius.academy/math/units/exponents_fractional_bases_and_exponents_practice/
1
Factor the base number to make it easier to solve
A LaTex expression showing 135 to the power of (1 over 3 )
a A LaTex expression showing (3 times 3 times 5) to the power of (1 over 3 )
b A LaTex expression showing (3 times 3 times 3 times 5 times 5) to the power of (1 over 3 )
c A LaTex expression showing (3 times 3 times 3 times 5 times 13) to the power of (1 over 3 )
d A LaTex expression showing (2 times 3 times 3 times 3 times 5) to the power of (1 over 3 )
e A LaTex expression showing (3 times 3 times 3 times 5) to the power of (1 over 3 )
f A LaTex expression showing (3 times 3 times 15) to the power of (1 over 3 )
2
Factor the base number to make it easier to solve
A LaTex expression showing 128 to the power of (1 over 3 )
a A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 2) to the power of (1 over 3 )
b A LaTex expression showing (2 times 2 times 2 times 4 times 2 times 2) to the power of (1 over 3 )
c A LaTex expression showing (2 times 2 times 2 times 2 times 4 times 2) to the power of (1 over 3 )
d A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 4) to the power of (1 over 3 )
e A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 2 times 2 times 11) to the power of (1 over 3 )
f A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 2 times 2) to the power of (1 over 3 )
3
Factor the base number to make it easier to solve
A LaTex expression showing 48 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 2 times 2 times 3 times 11) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2 times 3) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 2 times 2) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 2 times 2 times 3) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 2 times 6) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 2 times 2 times 3 times 13) to the power of (1 over 2 )
4
Factor the base number to make it easier to solve
A LaTex expression showing 75 to the power of (1 over 2 )
a A LaTex expression showing (3 times 3 times 5 times 5) to the power of (1 over 2 )
b A LaTex expression showing (3 times 5 times 5 times 7) to the power of (1 over 2 )
c A LaTex expression showing (3 times 5 times 5) to the power of (1 over 2 )
d A LaTex expression showing (3 times 5 times 5 times 13) to the power of (1 over 2 )
e A LaTex expression showing (3 times 5 times 5 times 11) to the power of (1 over 2 )
f A LaTex expression showing (2 times 3 times 5 times 5) to the power of (1 over 2 )
5
Factor the base number to make it easier to solve
A LaTex expression showing 32 to the power of (1 over 2 )
a A LaTex expression showing (2 times 2 times 2 times 2) to the power of (1 over 2 )
b A LaTex expression showing (2 times 2 times 2 times 2 times 2) to the power of (1 over 2 )
c A LaTex expression showing (2 times 2 times 2 times 4) to the power of (1 over 2 )
d A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 2) to the power of (1 over 2 )
e A LaTex expression showing (2 times 2 times 4 times 2) to the power of (1 over 2 )
f A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 7) to the power of (1 over 2 )
6
Factor the base number to make it easier to solve
A LaTex expression showing 162 to the power of (1 over 4 )
a A LaTex expression showing (2 times 3 times 3 times 3 times 3) to the power of (1 over 4 )
b A LaTex expression showing (2 times 2 times 3 times 3 times 3 times 3) to the power of (1 over 4 )
c A LaTex expression showing (2 times 9 times 3 times 3) to the power of (1 over 4 )
d A LaTex expression showing (2 times 3 times 3 times 9) to the power of (1 over 4 )
e A LaTex expression showing (2 times 3 times 3 times 3) to the power of (1 over 4 )
f A LaTex expression showing (2 times 3 times 3 times 3 times 3 times 3) to the power of (1 over 4 )
7
Factor the base number to make it easier to solve
A LaTex expression showing 48 to the power of (1 over 4 )
a A LaTex expression showing (2 times 2 times 2 times 3) to the power of (1 over 4 )
b A LaTex expression showing (2 times 4 times 2 times 3) to the power of (1 over 4 )
c A LaTex expression showing (2 times 2 times 2 times 2 times 2 times 3) to the power of (1 over 4 )
d A LaTex expression showing (2 times 2 times 2 times 2 times 3 times 5) to the power of (1 over 4 )
e A LaTex expression showing (2 times 2 times 2 times 2 times 3) to the power of (1 over 4 )
f A LaTex expression showing (2 times 2 times 2 times 2 times 3 times 13) to the power of (1 over 4 )